Search

Due to certain difficulties in solving fourth-order partial differential equations (PDEs) using localized methods, the given differential equation is normally split into two decoupled second order PDEs. Such an approach is only feasible for Dirichlet and Laplace boundary conditions. In this paper the localized method of particular solutions is applied to fourth-order PDEs directly using polynomial basis functions. The effectiveness of the proposed algorithms is demonstrated by considering four numerical examples.

Background/purpose Superspreading events (SSEs) are pivotal in the spread of SARS-CoV-2. This study aimed to investigate an SSE of COVID-19 in a hospital and explore the transmission dynamics and heterogeneity of SSE. Methods We performed contact tracing for all close contacts in a cluster. We did nasopharyngeal or throat swabbing for SARS-CoV-2 by real-time RT-PCR. Environmental survey was performed. The epidemiological and clinical characteristics of the SSE were studied. Results Patient 1 with congestive heart failure and cellulitis, who had onset of COVID-19 two weeks after hospitalization, was the index case. Patient 1 led to 8 confirmed cases, including four health care workers (HCW). Persons tested positive for SARS-CoV-2 were HCW (n = 4), patient 1's family (n = 2), an accompanying person of an un-infected in-patient (n = 1), and an in-patient admitted before the SSE (n = 1). The attack rate among the HCW was 3.2 % (4/127). Environmental survey confirmed contamination at the bed rails, mattresses, and sink in the room patient 1 stayed, suggesting fomite transmission. The index case's sputum remained positive on illness day 35. Except one asymptomatic patient, at least three patients acquired the infection from the index case at the pre-symptomatic period. The effective reproduction number (Rt) was 0.9 (8/9). Conclusion The host factor (heart failure, longer viral shedding), transmissibility of SARS-CoV-2 (Rt, pre-symptomatic transmission), and possible multiple modes of transmission altogether contributed to the SSE. Rapid response and advance deployment of multi-level protection in hospitals could mitigate COVID-19 transmission to one generation, thereby reducing its impact on the healthcare system.